Is there any situation where the electric field drop exponentially in free space? thanks
in free space? probably not...
but across a surface where total internal reflection occurs, some evanescent wave is transmitted, this wave is exponentially suppressed.
For electromagnetism, any near field amplitude component decays exponentially with distance.
For electrostatics, I'm not sure. There may be a way to construct a set of charges such that the multipole expansion looks like the series expansion for an exponential function, but I have never seen one.
Evanescent (exponentially decaying fields) can be produced by;
- Total internal reflection.
- Guided modes in a waveguide.
- An EM diffracting off a sub-wavelength aperture or obstacle (Near-field).
- Exciting a charged surface at resonance (surface plasmons).
> For electrostatics, I'm not sure. There may be a way to construct a set of charges such that the multipole expansion looks like the series expansion for an exponential function
Or put a dielectric with spatially varying dielectric constant around a point charge in a homocentric manner. This would eliminate the inverse square and introduce the exponential. Here it is:
E = 1/4πε(r) Q / r^2
if ε(r) = a * exp(br) / r^2
then you've got a decaying exponential effect.
E = E0 * exp(-br)
a field whose magnitude decays exponentially (either in 1-D or radially from some central point) has a non-zero divergence everywhere. so if by "free space" you mean no charge density, then I don't think such a field could exist anywhere in free space.
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